Equivalent Definitions of A Closed Set
In a topological space, a set is closed if and only if it coincides with its closure. Equivalently, a set is closed if and only if it contains all of its limit points.
This is not to be confused with a closed manifold.
Read more about this topic: Closed Set
Famous quotes containing the words equivalent, definitions, closed and/or set:
“Perhaps basketball and poetry have just a few things in common, but the most important is the possibility of transcendence. The opposite is labor. In writing, every writer knows when he or she is laboring to achieve an effect. You want to get from here to there, but find yourself willing it, forcing it. The equivalent in basketball is aiming your shot, a kind of strained and usually ineffective purposefulness. What you want is to be in some kind of flow, each next moment a discovery.”
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There have been many definitions of beauty in art. What is it? Beauty is what the untrained eyes consider abominable.”
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“Don: Why are they closed? They’re all closed, every one of them.
Pawnbroker: Sure they are. It’s Yom Kippur.
Don: It’s what?
Pawnbroker: It’s Yom Kippur, a Jewish holiday.
Don: It is? So what about Kelly’s and Gallagher’s?
Pawnbroker: They’re closed, too. We’ve got an agreement. They keep closed on Yom Kippur and we don’t open on St. Patrick’s.”
—Billy Wilder (b. 1906)
“The people always have some champion whom they set over them and nurse into greatness.... This and no other is the root from which a tyrant springs; when he first appears he is a protector.”
—Plato (c. 427–347 B.C.)